ABSTRACT: Recent attempts to explain quantum mechanics through a process of chaotic quantization, wherein quantum indeterminacy is viewed as chaotic behavior in a hidden, higher dimension, seem to require the existence of an additional time dimension. We investigate the possibility of formulating consistent physics in two time dimensions. The causal structure of 3+2 spacetime is preliminarily explored. Imposing the extra time dimension at the level of the commutation relations, we derive a Klein-Gordon equation and examine properties of its solutions. We then calculate modifications to the Coulomb potential caused by compactified and thermalized extra time dimensions, and show that while a compactified dimension leads to unphysical behavior, a thermalized extra time dimension does not. A model of the thermal time dimension is then developed, relying on the connection between the Fokker-Planck and Langevin equations. The model is solved to obtain probability distributions for the critical observables and a probabilistic representation for all other observables. We then explore possible connections between this theory and quantum mechanics.
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